Students are entering an auditorium at a constant rate .when the auditorium opens there are already 23 students sitting in it after it has been feeling for 10 minutes there are now 473 students in the auditorium. find average rate of change for the first 10 minutes how many students will be in the auditorium after 15 minutes of filling

There are 698 students in the auditorium after 15 minutes.

Given information:

Students are entering an auditorium at a constant rate.

At the initial phase, there are 23 students in the auditorium.

After it has been feeling for 10 minutes, there are now 473 students in the auditorium.

So, in 10 minutes, the number of students entered the auditorium is,

So, the rate at which the students are entering the auditorium will be,

So, after 15 minutes, the number of students in the auditorium will be,

Therefore, there are 698 students in the auditorium after 15 minutes.

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Let the rate be r, in units of students per minute.  After 0 minutes, we have 23 students, After t minutes, we have

s = rt + 23

When t=10 we have s=473

473 = 10r + 23

450 = 10r

r = 45 students per minute

Answer [first part]: 45 students per minute

When t=15, we get

s = 45(15) + 23 = 698

Answer [second part]: 698